Question

jamal places 1 - centimeter cubes in pairs. then he uses the pairs of cubes to make rows of different lengths. 1 pair 2 pairs 3 pairs a. what is the surface area of a row made of 30 pairs of cubes? show your work. sa = 2(60×1 + 60×1+1×1) = 2(60 + 60+1) = 2×121 = 242 solution 242 square - centimeters b. check your answer to problem 3a. show your work.

Explanation:

Step1: Determine the dimensions of the row

Each cube has side - length 1 cm. For 30 pairs of cubes, the length of the row is \(l = 60\) cm, width \(w=1\) cm and height \(h = 1\) cm.

Step2: Use the surface - area formula for a rectangular prism

The surface - area formula of a rectangular prism is \(SA=2(lw + lh+wh)\). Substitute \(l = 60\), \(w = 1\) and \(h = 1\) into the formula: \(SA=2(60\times1+60\times1 + 1\times1)\).

Step3: Simplify the expression inside the parentheses

First, calculate \(60\times1+60\times1 + 1\times1=60 + 60+1=121\).

Step4: Multiply by 2

Then, \(SA = 2\times121=242\) square centimeters.

for checking:

Step1: Analyze the surface - area components

The two ends of the row each have an area of \(1\times1 = 1\) square centimeter, so the total area of the two ends is \(2\times1=2\) square centimeters.
The two long sides of the row each have an area of \(60\times1=60\) square centimeters, so the total area of the two long sides is \(2\times60 = 120\) square centimeters.
The top and bottom of the row each have an area of \(60\times1=60\) square centimeters, so the total area of the top and bottom is \(2\times60=120\) square centimeters.

Step2: Sum up the areas

Adding these together: \(2+120 + 120=242\) square centimeters.

Answer:

242 square centimeters